Development of the Multicomponent Coupled-Cluster Theory for Investigation of Multiexcitonic Interactions

Abstract

Multicomponent systems are defined as chemical systems that require a quantum mechanical description of two or more different types of particles. Non-Born-Oppenheimer electron-nuclear interactions in molecules, electron-hole interactions in electronically excited nanoparticles, and electron-positron interactions are examples of physical systems that require a multicomponent quantum mechanical formalism. The central challenge in the theoretical treatment of multicomponent systems is capturing the many-body correlation effects that exist not only between particles of identical types (electron-electron) but also between particles of different types (electron-nuclear and electron-hole). In this work, the development and implementation of multicomponent coupled-cluster (mcCC) theory for treating particle-particle correlation in multicomponent systems are presented. This method provides a balanced treatment of many-particle correlation effects in a general multicomponent system while maintaining a size-consistent and size-extensive formalism. The coupled-cluster ansatz presented here is an extension of the electronic structure CCSD formulation for multicomponent systems and is defined as |ΨmcCC⟩ = eT1I+T2I+T1II+T2II+T11I,II+T12I,II+T21I,II+T22I,II|0I0II⟩. The cluster amplitudes in the mcCC wave function were obtained by projecting the mcCC Schrödinger equation onto a direct product space of singly and doubly excited states of type I and II particles and then solving the resulting mcCC equations iteratively. These equations were derived using an automated application of the generalized Wick’s theorem and were implemented using a computer-assisted source code generation approach. The applicability of the mcCC method was demonstrated by calculating ground state energies of multicomponent Hooke's atom and positronium hydride systems as well as by calculating exciton and biexciton binding energies in multiexcitonic systems. For each case, the mcCC results were benchmarked against full configuration interaction (FCI) calculations and were found to be in excellent agreement with the FCI results. The effect of neglecting certain classes of multicomponent connected excitation terms from the mcCC wave function was also investigated. The results from this study demonstrate that connected cluster operators that generate simultaneous excitation in type I and type II space are critical for capturing electron-hole correlation in multiexcitonic systems.

How intrinsic nuclear nonadiabaticity affects molecular structure, electronic density, and conformational stability: Insights from the multicomponent DFT calculations of Mu/H isotopologues

“…The key factor to a successful prediction of nuclear quantum effects by orbital‐based nonadiabatic ab initio procedures lies in the inclusion of electronic and nuclear correlation effects. This task has been extensively addressed in the form of multicomponent extensions of the configuration interaction , perturbation theory , coupled cluster formalism , and density functional theory (DFT) . The latter is indeed most intriguing due to its capabilities of being computationally “practical” and providing experimentally accurate results as revealed by the recent developments of the proton‐specific functionals .…”

The any particle molecular orbital approach: A short review of the theory and applications

“…We are currently working on the extension of the coupled cluster singles and doubles method with perturbative triples correction to the APMO formalism. Reference presents an extension of the coupled cluster singles doubles (CCSD) method to MC systems with two types of quantum species. The results presented in that work for model systems are in excellent agreement with FCI results.…”

“…[43,77] Furthermore, it has been found that compared to MC-FCI results the MC-MP2 approach is not capable of correcting the errors of the MC-HF reference.. [79] The triples correction to the APMO formalism. Reference [41] presents an extension of the coupled cluster singles doubles (CCSD) method to MC systems with two types of quantum species. The results presented in that work for model systems are in excellent agreement with FCI results.…”

“…One of the most studied properties of positron interactions with matter is the positron binding energy (PoBE). Experimental PoBEs have been reported for a number of atomic and molecular systems . The PoBE of an atomic or molecular system, X, can be calculated theoretically as the energy difference, …”

“…Experimental PoBEs have been reported for a number of atomic and molecular systems. [41,77,[113][114][115][116][117][118][119][120][121][122][123][124][125][126][127] The PoBE of an atomic or molecular system, X, can be calculated theoretically as the energy difference,…”